Combining Texts

All the ideas for 'fragments/reports', 'What are Sets and What are they For?' and 'Reply to Fifth Objections'

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16 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The empty set is something, not nothing! [Oliver/Smiley]
The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
Knowing the attributes is enough to reveal a substance [Descartes]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge
Our thinking about external things doesn't disprove the existence of innate ideas [Descartes]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
A blind man may still contain the idea of colour [Descartes]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
Necessary existence is a property which is uniquely part of God's essence [Descartes]
Possible existence is a perfection in the idea of a triangle [Descartes]